# Homework Help: Data networks question - shannon capacity formula

1. Aug 26, 2010

### bos1234

1. The problem statement, all variables and given/known data
A television picture is composed of approximately 300,000 individual picture elements
(pixels), each of which can attain ten different and distinguishable brightness levels (such as
black and shades of gray) for proper contrast. If for any picture element, the probability of
occurrence of the ten brightness levels are equal, and the frame rate is 30. Determine the
bandwidth of the video signal. Assume that a channel signal-to-noise ratio (SNR) of 30 dB is
required for proper reproduction of any picture.

2. Relevant equations
soln. says to use C=Blog_2(1+SNR)

how many bits/pixel?
log_210 bits/pixel=3.32 bits/pixel

C=300,000 x 30 x 3.32 = 30mbps

then proceeds to find B.

Why are they calculating bits/pixel? and where did the 30 come from? frame rate?

2. Aug 26, 2010

### xcvxcvvc

I think it's easiest to understand this by doing unit analysis of a single pixel and then multiplying the answer by the number of pixels (300k) because it's sort of like 300k parallel channels.

So we want bits per second. We have pixels per second (framerate). If we could get bits per pixel, we could multiply the two and have:
[pixels]/[second] *[bits]/[pixel] = [bits]/[second]

so you find bits/pixel, multiply it, and scale by how many parallel channels you have (300k)

3. Aug 26, 2010

### bos1234

thanks buddy. Got it now!
i didnt know frame rate was bits/second!